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Chapter 12: Problem 2

Which of the following terms does not represent electrical power in a circuit? (a) \(I^{2} R\) (b) \(I R^{2}\) (c) \(V I\) (d) \(V^{2} / R\)

Short Answer

Expert verified
Option (b) \( I R^{2} \) does not represent electrical power.

Step by step solution

01

Understand the formula for electrical power

Electrical power in a circuit, denoted as P, is commonly defined using the following formulas: \( P = I^2 R \), \( P = V I \), and \( P = \frac{V^2}{R} \). Here, \( I \) is the current, \( V \) is the voltage, and \( R \) is the resistance.
02

Identify the correct formulas

From the given options, identify which formulas match the standard definitions of electrical power. (a) \( I^{2} R \) matches \( P = I^2 R \). (b) \( I R^{2} \) does not match any of the standard definitions. (c) \( V I \) matches \( P = V I \). (d) \( \frac{V^{2}}{R} \) matches \( P = \frac{V^2}{R} \).
03

Identify the incorrect formula

From the options, determine that option (b) \( I R^{2} \) does not match any of the correct formulas for electrical power in a circuit.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ohm's Law
Ohm's Law is a fundamental principle in electrical engineering. It states the relationship between the current (I), voltage (V), and resistance (R) in an electrical circuit.
The law is mathematically represented as \( V = I \times R \).
This formula means that the voltage across a resistor is equal to the product of the current flowing through it and its resistance.
Understanding this relationship is crucial for analyzing and designing electrical circuits.

Here are some important points about Ohm's Law:
  • Current (I) is measured in amperes (A).
  • Voltage (V) is measured in volts (V).
  • Resistance (R) is measured in ohms (Ω).
Knowing Ohm's Law helps in solving many problems related to electrical circuits, including power calculations.
Electrical Circuits
An electrical circuit is a path in which electrons from a voltage or current source flow.
Understanding circuits is essential for working with electronics.
An electrical circuit is composed of various components like resistors, capacitors, inductors, and power sources that form a closed loop, providing a path for electrons to move.

Key elements of electrical circuits:
  • Power Source: Provides the necessary voltage to push current through the circuit. Examples include batteries and power supplies.
  • Resistors: Limit the flow of current and drop voltage within the circuit.
  • Conductors: Material, typically wires, that connect different components of the circuit and allow current to flow.

Circuits can be categorized in several ways:
  • Series Circuits: Components are connected end-to-end, so there is only one path for current flow.
  • Parallel Circuits: Components are connected across the same voltage source, providing multiple paths for current flow.
Proper understanding of these basic elements is essential in performing accurate power calculations.
Power Calculations
Power calculations are vital in electrical engineering to assess the performance and safety of electrical devices and systems.
Electrical power (P) is the rate at which electrical energy is transferred by an electric circuit. It is usually measured in watts (W).
The standard formulas for calculating power in a circuit are:
  • \( P = I^2 R \): Power is equal to the square of the current (I) multiplied by the resistance (R).
  • \( P = VI \): Power is the product of the voltage (V) across the components and the current (I) flowing through it.
  • \( P = \frac{V^2}{R} \): Power is the square of the voltage (V) divided by the resistance (R).

These formulas allow you to calculate power in different scenarios:
  • If you know the current and resistance, use \( P = I^2 R \).
  • If you know the voltage and current, use \( P = VI \).
  • If you know the voltage and resistance, use \( P = \frac{V^2}{R} \).
Using these formulas correctly helps in identifying the efficiency and energy consumption of electrical systems.

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Most popular questions from this chapter

A copper wire has diameter \(0.5 \mathrm{~mm}\) and resistivity of \(1.6 \times 10^{-8} \Omega \mathrm{m}\). What will be the length of this wire to make its resistance \(10 \Omega ?\) How much does the resistance change if the diameter is doubled?

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be- (a) \(1: 2\) (b) \(2: 1\) (c) \(1: 4\) (d) \(4: 1\)

The values of current \(I\) flowing in a given resistor for the corresponding values of potential difference \(V\) across the resistor are given below \(\begin{array}{l}I \text { (amperes) } & 0.5 & 1.0 & 2.0 & 3.0 & 4.0 \\ V \text { (volts) } & 1.6 & 3.4 & 6.7 & 10.2 & 13.2\end{array}\) Plot a graph between \(V\) and \(I\) and calculate the resistance of that resistor.

Show how you would connect three resistors, each of resistance \(6 \Omega\), so that the combination has a resistance of (i) \(9 \Omega\), (ii) \(4 \Omega\).

An electric heater of resistance \(8 \Omega\) draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.
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